Question

Given the following PARALLELOGRAM, find the measure of each angle below.

Answer 1

Answer:

m∠BEC = 65°

m∠DEC = 115°

m∠DAE = 78°

m∠ECD = 40°

m∠BAD = 118°

m∠ADC = 62°

Step-by-step explanation:

m∠BEC = 65°

Opposite angles formed by intersecting lines are congruent

m∠DEC = 180 - 65 = 115°

A straight line has a degree measure of 180

m∠DAE = 78°

Opposite interior angles of two parallel lines cut by a transversal are congruent

m∠ECD = 180 - [m∠DEC + 25] = 40°

Sum of angles inside triangle ECD has a measure of 180

m∠BAD = 78 + m∠ECD = 118°

Opposite angles of a parallelogram are congruent

2(m∠BAD) + 2(m∠ADC) = 360

118 + m∠ADC = 180

m∠ADC = 62°

Sum of angles inside a parallelogram = 360°